After years of preserving a fragile truce, the family that runs the Market Basket supermarket chain is again at war.

In the latest dispute, one faction of the family is trying to fire Arthur T. Demoulas as chief executive, arguing that he is spending money recklessly and steamrolling the board of directors. A special meeting to consider his fate is planned for July 18.

The campaign against Demoulas is being led by his first cousin, Arthur S. Demoulas, who has remained on the front lines of the fight over the company for more than 20 years.

While he contends it is time for change at the top, Arthur T. Demoulas says the business has remained strong during his tenure, recording income of $217 million in 2012 on $4 billion in revenue.